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The self-consistent diagrammatic method (SCDM) is utilized for the treatment of electronic excitation transfer in a substitutionally disordered system, which is induced by multipolar and exchange interactions. The multipolar rates were treated within the three-body approximation and the exchange transition rates were handled within the two-body approximation. We obtained analytical results in the short- and the long-time limits and numerical results over the entire time domain. These are utilized to explore the role of the range of the interaction and of the spatial dimensionality of the system on the validity of the SCDM. We also compare the SCDM with other methods and assess the validity of the higher-order approximations. The critical scrutiny of the SCDM method reveals that it can be successfully used for the interpretation of experiments for singlet exciton transfer in a low-concentration impurity band of 3D systems.